Electricity and Magnetism Flashcards
Electrical current is defined as what?
charge per unit time
I=Q/t, Q=coulombs t=seconds
Atom with net charge of either positive or negative
Ion
Negative ion
Anion
Positive Ion
Cation
The force required to move charges in a material
Voltage
Different names for voltage
Electromotive force(emf), Potential Difference
Volts formulas
V=W/C
W=work, Joules
C=Charge, Coulombs
*1 volt = 1 Joule/Coulomb
opposition or hindrance offered by the material to current flowing
Resistance
Ohm is named after whom?
Georg Simon Ohm
Resistance Formula
R=pL/A
p=resistivity
L=length
A=cross sectional area
What is the equivalent if 1 mil?
1/1000 inch
A Square mil is equal to?
pi/4 circular mil
Temperature effect on resistance formula
R2/R1=(|T|+t2)/(|T|+t1)
R2=R1(1+α(t2-t1))
α=1/(|T|+t1)
α=temperature coefficient of resistance at t1
T=inferred absolute zero temp
-234.5 for annealed copper
the property of material to aid or allow the flow of charge
Conductance
Conductance Formula
G=1/R
G=A/pL
Amount of work done in a circuit per unit time
Electrical Power
Power formulas
P=W/t P=QV/t P=IV P=V^2/R P=I^2R
What are the common resistivity(ρ) of:
Aluminum,
ρ = 2.6 x10^-8 ohm-m
What are the common resistivity(ρ) of:
Brass,
ρ = 6 x10^-8 ohm-m
What are the common resistivity(ρ) of:
Carbon,
ρ = 350 x10^-8 ohm-m
What are the common resistivity(ρ) of:
Nichrome,
ρ = 100 x10^-8 ohm-m
What are the common resistivity(ρ) of:
Silver
ρ = 1.5 x10^-8 ohm-m
What are the common resistivity(ρ) of:
Tungsten
ρ = 5.6 x10^-8 ohm-m
Temperature resistance coefficient (α, Not thermal expansion) of:
Annealed copper
α20 = 0.00393
Temperature resistance coefficient(α, Not thermal expansion) of
Nickel
α20=0.006
Temperature resistance coefficient of(α, Not thermal expansion)
Iron
α20=0.0055
engineering prefix
nano
1x10^-9
engineering prefix
pico
1x10^-12
engineering prefix
femto
1x10^-15
engineering prefix
atto
1x10^-18
A substance that possesses magnetism property and can attract iron and other ferromagnetic materials including ferrites (non metallic ferromagnetic materials)
Magnet
The place where magnet was discovered
Magnesia
the magnet is called _____ by ancient people
Lodestar (early guiding stars)
Iron oxide called magnetite (Fe3O4)
It is produced by electric current rather than a natural magnet
Electromagnetism
Who discovered the phenomenon of electromagnetism?
Hans Christian Oersted (april 21, 1820)
A property possessed by magnetic materials by the virtue of which residual magnetism is possible
Retentivity
The magnetism left after the removal of the magnetizing force
Residual Magnetism
The opposite of retentivity
Coercivity
It is required to counter retentivity to eliminate residual magnetism
Coercive force
How can a magnet lose its properties?
Tax evasion. jk, When it is heated, hammered, or dropped from a height
Tractive/Lifting force of a magnet formula
F=.5(AB^2)/u0
A=total area of contact, m^2
B=flux density, Wb/m^2 or T`
What is the first law of magnetism
Like poles repel and unlike poles attract
What is the second law of magnetism
A magnetic field always tends to arrange itself that the greatest number of lines of force are created
What is the domain theory of magnetism
The magnetic property of a material is due to the electron’s spin direction. In non-magnetic materials, the net magnetic field is zero since electron’s spin cancels each other, while in magnetic materials the magnetic fields are aligned thus forming small bar magnet
What is the molecular/Weber theory of Magnetism?
The molecules of a material are magnets themselves and magnetization consists of rearrangement of the molecules in a way that all north poles point in the same direction, as such with the south pole
Magnetic fields originate in _______ and terminate in _________
North pole, South pole
What do you call the property when the magnetic flux spreads in the air?
Fringing
What is Coulomb’s first law?
THe force of attraction or repulsion of two magnetic pole is directly proportional to their strength
What is Coulomb’s second law?
The force of attraction between two poles is inversely proportional to the square of the distance between them
Formula of Magnetic attraction
F = km1m2/r^2
k=1/4pi(u)
u=uo*ur
ur=relative permittivity
uo=absolute permittivity (constant 33)
The tendency of the magnetic lines of force is to ____________
take an easy magnetic path
___(yes/no) lines of force can cross each other
no
where is the right hand rule applicable?
when determining the magnetic field(conventional current flow)
Formula for Force in a current carrying conductor in a magnetic field
F = BILsin(theta)
B=flux density, Wb/m^2 o Tesla
I=current flowing in a conductor, Ampere
L-length of conductor, meters
Formula for Magnitude of flux surrounding a straight conductor
phi=14x10^-8IL*log(R/r) Wb
I=current, A
L=length, ft
R=radius of the desired limiting cylinder
r=radius of the conductor
Formula for Magnitude of flux between two parallel conductors
phi=28x10^-8IL*log(d-r)/r Wb
d=distance between the conductors
Formula for Force between two parallel conductors
F=2I1I2L/d x10^-7
I1,I2 = current in the conductors
L= length of the conductors, Meters
d=distance between the conductors, Meters
Direction of force between two parallel conductors
If same current direction, force is Attractive
If different direction, Force is repulsive
Formula for Force of attraction between poles of magnets
F = km1m2/d^2 Newtons
k=1/4piu0 x10^-7
m1,m2= magnetic pole strength, Wb
d=distance between poles, meters
Formula for Magnetic Flux Density
B=Φ/A, Wb/m^2
Φ= magnetic flux lines (in Wb) A= area (in m^2)
Reluctance Formula
R=L/uA, Ampere-turn/Wb
R=mmf/phi
L=length of the magnetic path, m
A=cross sectional area, m^2
u=permittivity of the material, H/m
Formula for Energy stored in a magnetic Circuit
1/2R(phi)^2
What is Hysteresis?
it is the internal friction of molecules, causing the heating of a material
What is Magnetomotive force?
The force required to establish magnetic field in a magnetic material
Magnetomotive force is dependent upon what?
Current flowing, A
and number of turns, Turns
1 Gilbert is equivalent to_____
0.4 (Ampere-Turn)
What is magnetizing force or magnetic field intensity?
magnetomotive force per unit length required to properly magnetize a given material
Formula for Magnetic field intensity formula?
H=mmf/L=NI/L ; (At/m)
It is the measure of how easily a magnetic field can be created in a material upon application of a magnetic force
Permeability (in Henrys per meter)
The reciprocal of permeability
Reluctivity
Hysteresis loss formula is also known as
Steinmetz’s Formula
What is the formula for Hysteresis Loss
Wh=nfBm^1.6
n=hysteresis coefficient
f=frequency, Hz
Bm=Maximum flux density, T
Formula for Ohm’s law in magnetism
phi=mmf/R ; Wb/Maxwell
The property of a magnetic material to allow easily magnetic flux to be established,
Permeance
Permeance Formula
1/R = Wb/At
Flux Density and Magnetic Field Intensity of an infinitely long straight conductor
B=uI/2pir
H=I/2pir
I - Current in conductor
Formulas for Ampere’s Circuital law in magnetism
Source of mmf
mmf=NI
mmf drops:
mmf=phi*R
mmf=Hl
Total Reluctance in series
Rt=R1+R2+R3…
Total Reluctance in Parallel
1/Rt=1/R1+1/R2…
Total FLux in Series
Phi(total)=phi(1)=phi(2)=phi(3)
Total Flux in Parallel
Phi(total)=Phi1 + Phi2
Who discovered Charge?
Benjamin Franklin
Where and when was “electricity” coined?
600BC, Greece
“electricity” comes from the word _____
Amber
When you rub Silk on glass, the glass is (+ , - ) charged
Positively charged
Another term for a positively charged material
Vitreous
When you rub Fur on Rubber, the Rubber is (+ , - ) charged
Negatively Charged
Another term for a negatively charged material
Resinous
A machine used to produce a static charge
Van de Graff Generator
Coloumb’s Constant(k)
K = 1/(4πεo) = 9 x 10^9 Nm^2/C^2
Unit of Coloumb’s Constant (k)
Nm^2/C^2
Unit of Permittivity (ε)
C^2/(Nm^2)
or
F/m
The Electrostatic force is ____ times greater than the gravitational force of attraction felt by two particles
10^36
Unit of Electric Field Intensity
Volts / m or N / Coloumb
More common as V/m
A material that emits equally opposing charges
Dipole
an electric field emitted by a dipole will have a point, with an E-Field intensity equal to zero, Located at ________
Nowhere
no point in an E-Field of a dipole exists an Intensity of zero
The Force Vector and the E-Field Vector are always _________
Parallel to each other (points at the same direction
Gauss Law
Flux = ∑(Q / εo)
Q - Charges inside a closed surface
What is the E-Field observed when a Charge Q is Distributed uniformly on a spherical surface?
The E-Field observed at any point outside the sphere will look like an E-Field emitted by a charge in a single point, as if the charge was only concentrated at the center of that sphere
What is the E-Field observed inside a spherical surface with a uniformly distributed charge over its surface?
E-Field is 0
Charge(Q) inside is 0 as well
What is the E-Field observed in the presence of an infinite sheet of charge
Assuming that the sheet is infinitely large, the E-Field Intensity observed AT ANY POINT IN SPACE is:
E = ρs / 2εo
ρs - Surface Charge Density (Coloumb / m^2)
εo - Permittivity of Free Space
E-Field BETWEEN equally, but oppositely charged plates
E = ρs / εo
ρs - Surface Charge Density (Coloumb / m^2)
εo - Permittivity of Free Space
E-Field OUTSIDE equally, but oppositely charged plates
E = 0
except at the ends of the plates, where the fringe field exists
What does it mean when Coloumb’s force is Conservative?
If a particle moves around an E-Field, and will return to its initial position, the summation of work done by the charge to oppose the E-Field as it moves, minus the work done by the E-Field to the particle when the particle moves along with the E-Field, is equal to zero
Formula for Work done by a particle from point A to B under the influence of an E-Field
W(AB) = ΔPE = Q(test) (VA - VB)
Q(test) - Charge of the moving particle
VA - Voltage @ Point A
VB - Voltage @ Point B
Formula for the Speed of a particle from point A to B under the influence of an E-Field
Shift solve for ‘v’:
ΔPE = ΔKE
W(AB) = 0.5mv^2
Q(test)x(V(AB)) = 0.5m(v)^2
Q(test) - Charge of the moving particle
V(AB) = (VA - VB)
VA - Voltage @ Point A
VB - Voltage @ Point B
The Locus of points around a charge where the Electric Field Intensity and Voltage is equal
Equipotential Lines
Equipotential lines are (Parallel/Perpendicular) to the Electric Field Lines
Perpendicular
The Electric Field is obtained by performing a ________ Operator on the __________
Gradient Operator on the Voltage
E(vector) = - ∇(Voltage)
Note: Gradient transforms a scalar field into a vector field
Formula for Capacitance between two parallel plates
C = (εo A) / d
“Seed”
A - Area of plates
d -Distance between plates
The electric field inside a conductor is ____
E = 0 V/m
Charges in a conductor will ______ on the outer surface of a conductor
Uniformly Distribute
Inside an enclosed surface made out of a conductor, there is no ________ or ________
Charge or Electric Field
Conductors throughout its material is said to be __________ in terms of voltage
Equipotential
An enclosed surface build for the purpose of electrostatic shielding
Faraday’s Cage
What happens when you introduce a charge inside a Faraday’s Cage?
Ex. if a positive charge is placed inside, the inner surface of the Faraday’s Cage will be Negatively, but Equally Charged as that of the positive charge inside
but since conductors(The faraday cage) are equipotential (E = 0), the outer surface of the cage will be positively charged, as equally as the negatively charged inner surface
What Electric Field Intensity is Required for a High Voltage Breakdown(in air)?
3 x 10^6 V/m
A Famous example of A high Voltage Breakdown (An electric field of 3x10^6 V/m) is the weather phenomenon called _________
Lightning
When a High Voltage Breakdown paired with a continuous flow of current occurs, it causes the ________
Corona Effect / St. Elmo’s Fire
A ______ Magnet is always a permanent magnet
Natural
An _______ Magnet requires the phenomenon of electromagnetism
Artificial
When the Relative Permeability of a material (μr) is Greater than or equal to 100, the material is said to be ________
Ferromagnetic
When the Relative Permeability of a material (μr) is Slightly greater than 1, the material is said to be ________
Paramagnetic
When the Relative Permeability of a material (μr) is Slightly less than 1, the material is said to be ________
Diamagnetic
The Most Famous Diamagnetic Material is ________
Copper
A Diamagnetic Material (Deflects/Attracts) Magnetic Flux Lines
Deflects
When the Relative Permeability of a material (μr) is equal to 1, the material is said to be ________
Non-Magnetic
1 Weber is equal to ________ Maxwells
1 Wb = 1 x 10^8 Mx
The CGS equivalent of Tesla (Wb/m^2)
GAUSS:
1 Gauss = 1 Mx/cm^2
THEORY: A coil of wire in the presence of a changing magnetic field will “induce” a voltage across the coil
FARADAY’S LAW
V = NdΦ/dt
N - number of turns
dΦ - change in Magnetic Flux Lines
dt - as time changes
Will a coil of wire in the presence of a static magnetic field induce a voltage?
no
based on V = NdΦ/dt, no change in dΦ means no voltage
Alternative Magnetic Flux Density Formula
B = μH
B - Magnetic Flux Density (Wb/m^2)
μ - Permeability (μ = μrμo) (in Henrys/m)
H - Magnetic Field Intensity (in Henrys or Ampere-turn/meter)
Unit for Permeability of Free Space
μo - 4π x 10^-7 H/m
Unit is in Henrys / meter (H/m)
Formula for alternative interpretation of Faraday’s Law
V = L (di/dt)
V - voltage induced in a coil
L - Inductance of Coil (in Henrys)
di - Change in Current
dt - change in time
Will there be an induced voltage when the current through a coil is DC?
No
based on V = L (di/dt), no change in di means no voltage
Combining the two equations for Faraday’s Law gives this equation:
V = NdΦ/dt And V = L (di/dt)
NdΦ/dt = L (di/dt) ∫NdΦ/dt = ∫L (di/dt)
Final Equation:
NΦ = Li
N - Number of Turns in a coil
Φ - Magnetic Flux lines
L - Inductance
i - Current
Combining:
NΦ = Li, B = μH, H = mmf/ l, mmf = Ni and B=Φ/A
will give the formula for __________
INDUCTANCE FORMULA: B = μH --------EQ 1 B=Φ/A ---------EQ 2 NΦ = Li >>>>>>> Φ = Li/N ----EQ 3 H = mmf/ l --------EQ 4 mmf = Ni --------EQ 5
EQ1 + EQ2
Φ/A = μH»_space;»»»> ADD EQ3 (substitute Φ)
Li/NA = μH»_space;»»» ADD EQ4 (substitute H)
Li/NA = μ mmf/ l»_space;»»> ADD EQ5 (substitute mmf)
Li/NA = μ . Ni/ l
FINAL FORMULA:
L = μ(N²)A / l (in Henrys)
“LUNAL”
μ - Permeability
l - length of inductor coil
N - Number of Turns
A - Area
THEORY: a supplement to Faraday’s Law, where it indicates that the polarity the induced EMF in the presence of a changing magnetic field
LENZ LAW:
V = -NdΦ/dt
The effect observed when electrons are pushed to one side of a conductor that carries current, due to the presence of a magnetic field, Polarizing the conductor, making one side positive, and another negative, that results to a voltage across the width of the conductor
Hall Effect
Formula for the Hall Voltage in the conductor due to the Hall Effect
V(hall) = I*B / [n(qe)d]
I - Current in conductor(Amperes)
B - Magnetic Flux Density (in Tesla)
qe - electron charge (-1.6 x 10^-19 Coloumbs)
d - Thickness of conductor (not Area)
n - Volumetric Electron Density (#e- / m^3)
Formula for Electron Density(n) of a material
n = ρ(NA) / MM
ρ - Density of Conductor
NA - Avogadro’s Number (6.022 x 10^23 particles/mole)
MM - (Molar Mass (g/mol))
Electron Density(n) for copper
n(copper) =8.5 x 10^28 (in #e- / m^3)
Formula for Drift Velocity ¯_(ツ)_/¯
Vd = I / [n(qe)A]
I - Current in conductor(Amperes)
qe - electron charge (-1.6 x 10^-19 Coloumbs)
A - Cross Sectional Area of conductor
n - Volumetric Electron Density (#e- / m^3)
